Answers
The components of the position vector of the rabbit's final location r₂, x and r₂, y is 36.77 m.
How to calculate position?To find the final location of the rabbit, calculate the displacement of the rabbit, which is given by the product of average velocity and time.
r₂, x = 1, + vx x t = -18.7 - 2.17 x 10.7 = -43.77 m
r₂, y = 1, + vy x t = 21.5 + 1.71 x 10.7 = 36.77 m
Therefore, the components of the position vector of the rabbit's final location are r2x = -43.77 m and r2y = 36.77 m.
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Related Questions
During a typical afternoon thunderstorm in the summer, an area of 57.0 km2 receives 5.81 X 10^8 gal of rain in 18 min. How many inches of rain fell during this 18 min period?
Answers
1.5189 inches of rain fell during this 18 min period.
What is the unit of rainfall?The amount of rain that fell in total over a specific time period, measured in millimeters, is the most typical rainfall measurement.
Area = 57.0 km² = 57.0 × 1000 × 1000 m²
Volume of water = 5.81 × 10⁸ gallon = 5.81 × 10⁸ × 0.00378541 m³ = 2199323.21 m³
Hence, the height of the rain water
= (2199323.21 m³) ÷ (57.0 × 1000 × 1000 m²)
= 0.03858 m
= 0.03858 × 39.3701 inch
= 1.5189 inch
So, 1.5189 inches of rain fell during this 18 min period.
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How does understanding the formation of the sun contribute to understnading how it releases electromagnetic energy, including sunlight, which allows Earth to be what it is today?
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Radiant energy that moves in waves at the speed of light is known as electromagnetic energy. Radiant energy, electromagnetic radiation, electromagnetic waves, light, or the movement of radiation are other names for it.
What is Electromagnetic waves?James Clerk Maxwell, a 19th-century physicist whose research had a major impact on the development of quantum mechanics, discovered electromagnetic radiation.
We can think of electromagnetic energy or radiation functioning similarly to a typical ocean wave in terms of how it operates. The radiation is the water in this analogy.
Radiation from an electromagnetic field can transfer heat. Heat, energy, or light waves are transmitted from one place to another across a vacuum or a medium using electromagnetic waves.
Therefore, Radiant energy that moves in waves at the speed of light is known as electromagnetic energy. Radiant energy, electromagnetic radiation, electromagnetic waves, light, or the movement of radiation are other names for it.
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The lowest pressure ever obtained in a laboratory setting is 4.0×10−11 Pa. At this pressure, how many molecules of air would there be in a 50 Celsius experimental chamber with a volume of 0.060 m3?
Answers
There would be 5.38 × 10¹⁹ number of molecules of air at that condition.
What is ideal gas?A theoretical gas known as an ideal gas is made up of several randomly moving point particles with no interparticle interactions.
Because it abides by the ideal gas law, a condensed equation of state, and is amenable to statistical mechanics analysis, the ideal gas concept is helpful.
The amount of air = PV/RT
= (4.0 × 10 ⁻¹¹× 0.060)/ 8.314 ×(273 + 50) mole
= 8.93714 × 10⁻⁵ moles.
molecules of air would there be = 8.93714 v × 6.023 × 10²³ = 5.38 × 10¹⁹
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An orange of mass 125 g falls from a branch to the ground 3.50 m below. (a) Relative to the ground, what is the gravitational potential energy of the orange on the branch? On the ground? (b) Relative to the branch, what is the gravitational potential energy of the orange on the branch? On the ground? J (c) During the orange's fall, what is its change in gravitational potential energy relative to the ground? Relative to the branch?
Answers
(a) Relative to the ground, the gravitational potential energy of the orange on the branch is 4.29 J and on ground is 0 J.
(b) ) Relative to the branch, the gravitational potential energy of the orange on the branch is 0 J and on ground is 4.29 J.
(c) The change in potential energy relative to the ground is -4.29 J and relative to the branch is 0 J.
What is the gravitational potential energy?Relative to the ground, the gravitational potential energy of the orange on the branch is calculated as follows;
P.E = mgh
where;
m is the mass of the orangeh is the height of the branch above the groundg is acceleration due to gravityP.E = 0.125 kg x 9.8 m/s² x 3.5
P.E = 4.29 J
The gravitational potential energy of the orange on the ground is calculated as follows;
P.E = mgh
P.E = m x g x 0 m
P.E = 0 J
The change in potential energy = final potential energy - initial potential energy
change in potential energy relative to ground = 0 J - 4.29 J = - 4.29 J
change in potential energy relative to branch = 4.29 J - 4.29 J = 0
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A hot-air balloonist, rising vertically with a constant velocity of magnitude v=5.00 m/s, releases a sandbag at an instant when the balloon is a height h=40.0m above the ground (Figure 1). After it is released, the sandbag is in free fall. For the questions that follow, take the origin of the coordinate system used for measuring displacements to be at the ground, and upward displacements to be positive.
A) Compute the position of the sandbag at a time 0.245 s after its release.
B) Compute the magnitude of the velocity of the sandbag at a time 0.245s after its release.
C) Determine the direction of the velocity of the sandbag at a time 0.245 s after its release.
D) Compute the position of the sandbag at a time 1.15 s after its release.
E) Compute the magnitude of the velocity of the sandbag at a time 1.15 s after its release.
F) Determine the direction of the velocity of the sandbag at a time 1.15 s after its release.
Answers
a. The position of the sandbag at a time 0.245 s after its release is 39.706 m from the ground.
b. The magnitude of the velocity of the sandbag at a time 0.245 s after its release is 2.4 m/s.
c. The direction of the velocity of the sandbag at a time 0.245 s after its release is to the ground.
d. The position of the sandbag at a time 1.15 s after its release is 33.52 m from the ground.
e. The magnitude of the velocity of the sandbag at a time 1.15 s after its release is 11.27 m/s.
f. The direction of the velocity of the sandbag at a time 1.15 s after its release is to the ground.
According to the free-fall motion, when an object is released without an initial velocity from a certain height the object will experience acceleration due to the gravitational force of the earth. The non-uniform motion formula
v = u + at
d = (u × t) + 0.5at²
u = initial velocity = 0t = time (s)a = accelerationg = acceleration due to gravity
a = g = - 9.8 m/s²
Negative because moves downward
The formula for free-fall motion become
v = u + at ⇒ v = gt
d = (u × t) + 0.5at² ⇒ d = 0.5gt²
When the sandbag is released by the balloon at h = 40.0 m, it moves in a free-fall motion.
At t = 0.245 s
The sandbag traveledd = 0.5gt² = 0.5 × - 9.8 × 0.245² = - 4.9 × 0.060025
d = - 0.294 mThe position
h + d = 40.0 - 0.294 m = 39.706 m from groundThe velocity
v = gt = - 9.8 × 0.245
v = - 2.401 m/s
v = - 2.4 m/s
with direction to the ground
At t = 1.15 s
The sandbag traveledd = 0.5gt² = 0.5 × - 9.8 × 1.15² = - 4.9 × 1.3225
d = - 6.48 mThe position
h + d = 40.0 - 6.48 m = 33.52 m from groundThe velocity
v = gt = - 9.8 × 1.15
v = - 11.27 m/s
with direction to the ground
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A sprinter with a mass of 70 kg accelerates at a rate of 5 m/s2. What force is the sprinter exerting?
Answers
Answer:
The force exerted by the sprinter can be calculated using Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration:
F = m * a
where:
F is the force
m is the mass of the object (70 kg)
a is the acceleration (5 m/s^2)
Plugging in the values, we get:
F = 70 kg * 5 m/s^2
F = 350 N
So, the sprinter is exerting a force of 350 N. This is the force that the sprinter's legs are applying to the ground, propelling them forward and producing the acceleration.
A piece of lithium goes from 65 Celsius to 200 Celsius what state of matter would be expected to be in 
Answers
At 65°C, lithium is a solid. At 200°C, liquid would be the state of matter.
What is state of matter?State of matter refers to the physical form in which a substance exists. There are four main states of matter: solid, liquid, gas, and plasma. In a solid, particles are closely packed together and have a fixed shape and volume. In a liquid, particles are close together but can flow and take the shape of their container. In a gas, particles are widely spread out and have a much larger volume and take the shape and volume of their container. In plasma, particles are highly ionized and have unique electrical and thermal properties.
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A bird is flying due east. Its distance from a tall building is given by x(t)=29.0m+(12.8m/s)t−(0.0450m/s3)t3. What is the instantaneous velocity of the bird when t = 8.0s?
Answers
The velocity of the bird would be 4.16 m/s².
What is instantaneous velocity?The velocity of a body at any specific instant of time is called instantaneous velocity. Mathematically, we can write -{v} = dx/dt
Given is that a bird is flying due east. Its distance from a tall building is given by -
x{t} = 29 + 12.8t - 0.0450t³
Instantaneous velocity is given by -
{v} = dx/dt ... Eq { 1 }
Now -
v = dx/dt = d/dt (29 + 12.8t - 0.0450t³)
v = dx/dt = 0 + 12.8 - (3 x 0.0450t²)
v = dx/dt = 12.8 - 0.135t²
v{8} = dx/dt = 12.8 - 0.135 x 8 x 8
v{8} = dx/dt = 12.8 - 8.64
v{8} = dx/dt = 4.16
Therefore, the velocity of the bird would be 4.16 m/s².
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A very thin sheet of brass contains two thin parallel slits. When a laser beam shines on these slits at normal incidence and room temperature (20.0 ∘C ), the first interference dark fringes occur at ± 26.6∘ from the original direction of the laser beam when viewed from some distance. If this sheet is now slowly heated up to 135 ∘C , by how many degrees do these dark fringes change position? Coefficient of linear expansion for brass is α=2.0×10−5(∘C)−1 . Ignore any effects that might occur due to change in the thickness of the slits. (Hint: Since thermal expansion normally produces very small changes in length, you can use differentials to find the change in the angle.)
Answers
We do not know the value of L0 and d, we cannot calculate the exact change in angle. However, we can find the order of magnitude of Δθ by using the values given in the problem.
How solve the problem?The change in the angle can be calculated by using the formula for linear expansion: ΔL = L0 * α * ΔT, where ΔL is the change in length, L0 is the initial length, α is the coefficient of linear expansion, and ΔT is the change in temperature.
We can assume that the distance between the two slits is the length L0. The change in length ΔL will cause a change in the angle of the dark fringes, which can be calculated using the formula: Δθ = ΔL / d, where Δθ is the change in angle and d is the distance from the slits to the observation point.
So, ΔL = L0 * α * ΔT = L0 * α * (135 - 20)
Δθ = ΔL / d
Substituting the given values, we get:
Δθ = L0 * α * (135 - 20) / d
= L0 * 2.0 x 10^-5 * 115 / d
Since we do not know the value of L0 and d, we cannot calculate the exact change in angle. However, we can find the order of magnitude of Δθ by using the values given in the problem.
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Please answer this question
Answers
A mechatronic system can be a common household appliance such as a washing machine, a car engine, or an industrial production line.
Using the parts above, what is the washing machine component?For example, in a washing machine, the actuators could be the DC motors that control the drum's rotation, the solenoids that control water flow, and the voice coils that control the drum's position.
The sensors could be switches that detect the lid's position, the photoelectrics that detect the presence of clothes, and the potentiometers that measure the drum's position.
The input signal conditioning and interfacing could be the discrete circuits that filter and amplify the signals from the sensors.
The graphical displays could be the LED lights that indicate the status of the machine, and the output signal conditioning and interfacing could be the amplifiers and power transistors that control the actuators.
The digital control architecture could be the microcontroller that implements the control algorithms and sequences the operations of the machine.
This is just an example of how to map a mechatronic system, and the components and their arrangement can vary greatly depending on the specific system being analyzed.
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